Entropy and the variability of dependence: System of profound knowledge (SPK) and induced entropy copula as a measure of variability for copula density

Deming’s System of Profound Knowledge (SPK) is a framework for creating, disseminating, and applying knowledge in business. One of its basic principles is the knowledge of variation. SPK is based on a systemic approach in which each part of the system is interconnected. Process control seeks to determine whether a process is in control, meaning whether the distribution of some critical measured variable is stable. Complex systems may vary through time and their variability can be measured by its entropy and its interrelatedness. The entropy copula or interrelatedness is interpreted as a measure of reduction of independence measured by the entropy of independent variables. This paper provides the expression of the entropy copula for multivariate t distribution and introduces the concept of induced entropy copula as a measure of variability for copula densities. A test for uncorrelatedness based on the entropy copula is also developed. A manufacturing example, using multivariate control chart, is analyzed using the entropy copula approach. Tables are provided in the appendix for testing at different significance levels.